Star of David

This blog has reference to the star of David drawn by latAjI (http://ikolam.com/node/297?p=5851) and my response to it. The star of David is the centre piece of the Israeli flag. I mentioned this in a different context while explaining the hexagonal yantras (http://ikolam.com/node/5387?p=1930). Before trying to draw the interpenetrating star of David, we must learn how to construct a Mobius strip (http://en.wikipedia.org/wiki/Möbius_strip ). Mobius strip is a ribbon with only one surface. Normally a strip of paper or a ribbon has two surfaces, But Mobius strip has only one surface. How is this possible? Let us take a paper strip ABCD as shown in the figure. If we join AB and CD, then we get a cylindrical ribbon with two surfaces. However, if we twist the paper by half a turn and join AB with DC, we get a Mobius strip. If an ant starts from one point on this surface, it can crawl on both the surfaces of the strip and return to the point of start! That is the beauty of this strip as it has no beginning or end. With this property in view, I translated this in Sanskrit as ananta kAnchi (endless belt, kAnchi normally means the girdle worn around the waist). I described elsewhere how to write poetry on a Mobius strip (http://www.eemaata.com/em/issues/200903/1408.html). Even if you do not know how to read Telugu, it may still be beneficial to see the pictures there. The Mobius strip has the property of directionality. If the half twist is like the way Indian women normally wear the sari, then it is positive, otherwise negative. Let us construct a Mobius strip and bend it into a triangular form. Let us have another Mobius strip (of the same direction and a different direction) ready without joining the ends. Let us take this inside and outside continuously through the first one as shown and finally join it. Now we have an interpenetrating star of David with two Mobius strips. I have shown both the cases (strips with the same helical rotation and opposite rotations). Also are shown strips with the same colour on both the sides and different colours on the two sides of the strip. Symmetry-wise, the normal star of David drawn with lines has six-fold (60 degree rotation) and six mirrors at 30 degree angle. But the star of David made with two Mobius strips has a lower symmetry. I will leave it as an exercise to find the symmetry properties of this. Regards! - mOhana